–81, 108, –144, 192,. Which formula can be used to describe the sequence?.

At a coffee shop, out of the orders of the first 100 customers, the probability that the customer ordered the medium, given that they ordered a cold drink is 0.48 or 48%

What is probability?

Probability is the possibility of occurence of a certain event. Probability of any event lies between zero and 1. zero indicates that it is an impossible event whereas one indicates it is a certain event. To calculate probability we divide the number of favourable outcomes of an event by the total possible outcomes or sample space for that event. Conditional-probability refers to the occurence of any event (B) given that (only under) the condition that event  (A) has occured.

Conditional probability of event B given that event A has occured is given by: P(B | A) = {P(A ∩ B) ÷ P (A)}

Here we need to find the probability that the customer ordered the medium, given that they ordered a cold drink,

The customers who ordered cold drink are:

small & cold=8

medium and cold=12

large & cold=5

Total customers who ordered cold=8+12+5

                                                          =25

Probability who ordered cold = \(\frac{favourable outcomes}{total outcomes}\)

                                      P(cold) = \(\frac{25}{100}\)

And the customers who ordered only medium & cold=12

Probability of customers who ordered medium & cold= \(\frac{favourable outcomes}{total outcomes}\)

                                                          P(medium ∩ cold)  =\(\frac{12}{100}\)

Now, applying both the conditions together,

P(medium | cold) = {P(medium ∩ cold)} ÷ P (cold)

                            =  \(\frac{12}{100}\) ÷  \(\frac{25}{100}\)

                             =\(\frac{12}{25}\)

                             =0.48

On converting into percentage: 0.48 x 100=48%

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The probability that a customer ordered a medium drink, given that they ordered a cold drink, is 0.48.

What is probability?

Probability is the possibility of occurrence of a certain event. Probability of any event lies between zero and 1. zero indicates that it is an impossible event whereas one indicates it is a certain event.

To find the probability that a customer ordered a medium drink, given that they ordered a cold drink, we need to use Bayes' theorem.

First, let's calculate the probability of a customer ordering a cold drink:

P(cold) = (8+12+5)/100 = 25/100 = 0.25

Next, let's calculate the probability of a customer ordering a medium drink and a cold drink:

P(medium ∩ cold) = 12/100

Finally, we can use Bayes' theorem:

P(medium| cold) = P(medium ∩ cold)/P(cold) = (12/100)/(25/100) = 12/25 = 0.48

Therefore, the probability that a customer ordered a medium drink, given that they ordered a cold drink, is 0.48.

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The answer is x= 2/3

:) <3

Answer:

40%

Step-by-step explanation:

The ratio of the leading coefficients and the equation of the horizontal asymptote is degree of numerator and denominator is equal.

The term coefficients in math is defined as the coefficient of the term of highest degree in a polynomial.

Here we have given that  the ratio of the leading coefficients and the equation of the horizontal asymptote.

The term horizontal asymptote is known as  a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

As we all know that if the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote is equal to the ratio of the leading coefficients.

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Answer: 1.48

Step-by-step explanation:

I divided 4.44 by 3 and got 1.48 simple math ...

Answer:

$28.80

Step-by-step explanation:

16 times 0.8 = 12.8 + 16 = 28.80

Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

The age of Michael as of now is 6 years old as the age pf Norman will be 12 years. So option (B) 6 is correct answer.

Let N = Norman’s age now; (N + 6) = Norman’s age in 6 years.

Let M = Michael’s age now; (M + 6) = Michael’s age in 6 years.

Translate the first two sentences into equations. Note that the second equation deals with Norman and Michael’s ages in 6 years:

N=M+12

(N+6)=2(M+6)

The question asks for M, so substitute (M + 12) for N in the second equation:

(M+12)+6=2(M+6)

M+18=2M+12

M=6

Therefore, the age of Michael as of now is 6 years old. So option (B) 6 is correct answer.

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The gradient field of the function is given by grad f = 6x i + 8y j + k and it passes through the plane z = 1/4, where k = 1.

The given function is f(x, y, z) = 3x² + 4y² + 2z² and it is required to find the gradient field of this function, where the gradient field is Vf = + k. Therefore, the solution is given below.

To determine the gradient of the given function, we must first compute its partial derivatives with respect to x, y, and z.  So, let's calculate the partial derivatives of the given function first:

∂f/∂x = 6x∂f/∂y = 8y∂f/∂z = 4z

The gradient vector field is as follows:

grad f = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k= 6x i + 8y j + 4z k

Now, as given, the gradient field is Vf = + k. Thus, we only have the k-component of the vector field and no i or j-component.

Therefore, comparing the k-component of the gradient vector field with Vf, we get:

4z = 1 (As Vf = k, we only need to compare the k-components.)

Or z = 1/4

Hence, the gradient field of the function is given by grad f = 6x i + 8y j + k and it passes through the plane z = 1/4, where k = 1.

The gradient field indicates that the function is increasing in all directions. In addition, we can see that the z-component of the gradient field is constant.

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The position of the mass in the undamped spring-mass system can be represented by the equation u(t) = (A cos(ωt) + B sin(ωt)) / k. Therefore, position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

In this case, the external force acting on the system is 108 cos(4t) lb. To determine the position of the mass, we need to solve the differential equation that represents the motion of the system.

Using Newton's second law, F = ma, and considering that the mass m = 24 lb, the equation becomes:

24 * d^2u/dt^2 = 108 cos(4t)

Simplifying, we have:

d^2u/dt^2 = 4.5 cos(4t)

This is a second-order linear homogeneous differential equation with a constant coefficient. The solution to this equation will be a linear combination of the homogeneous and particular solutions.

The homogeneous solution, representing the free oscillation of the system, is u_h(t) = C1 cos(2t) + C2 sin(2t).

The particular solution, representing the forced motion caused by the external force, can be assumed in the form u_p(t) = A cos(4t) + B sin(4t).

By substituting u_p(t) into the differential equation, we can determine the values of A and B.

Solving the differential equation for the particular solution, we find:

A = 18 and B = 0

The complete solution for the position of the mass in feet is:

u(t) = (18 cos(4t)) / 4

Simplifying further, we get:

u(t) = 4.5 cos(4t)

Therefore, the position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

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The coordinates of point C are (17, -1).

let say a line have two points A (x1,y1) and B(x2,y2)

slope of line AB = (y2 - y1) / (x2 - x1)

Now given that  points B, C, and D are collinear, then they lie on the same straight line. This means that the slope of the line passing through any two of the points will be the same as the slope of the line passing through the other two points. We can use this fact to find the value of x.

The slope which is between points B and C is:

slope of line BC = (y2 - y1) / (x2 - x1) = (-1 - 7) / (x - (-1)) = -8 / (x + 1)

The slope which is between points C and D is:

slope of line CD = (y2 - y1) / (x2 - x1) = (8 - (-1)) / (1 - x) = (9) / (1 - x)

Since B, C, and D are collinear, slope of BC = slope of CD. Therefore:

-8/(x+1) = 9/(1-x)

by solving the x, we get:

-8(1 - x) = 9(x + 1)

-8+8x=9x + 9

x = 17

So, the coordinates of point C are (17, -1).

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Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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There is a circumference of 69.167 miles per degree of latitude.

Firstly, we assume that the earth is a spherical form to simplify calculations as spheres have constant radii of curvature, because the real form of the planet is similar to a oblate spheroid, a kind of ellipsoid. In addition, the circular arc (s), in miles, is directly proportional to the measure of the central angle (θ), in degrees, that is:

s ∝ θ

s = k · θ         (1)

Where k is the constant of proportionality, in miles.

Now we eliminate the constant of proportionality and we calculate the circular arc afterwards:

s / 24900 mi = 1° / 360°

s = 1 / 360 × 24900 mi

s = 69.167 mi

There is a circumference of 69.167 miles per degree of latitude.

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Answer:

46

Step-by-step explanation:

Since we know the value of the variable c, we can substitute 20 for c

2c + 6

2(20) + 6

40 + 6

46

Answer:

(2x + 7) feet

Step-by-step explanation:

I'm guessing the expression there is

4x² + 28x + 49

4x² +14x +14x +49

Factorize

2x ( 2x + 7) +7( 2x + 7)

(2x + 7)²

Area = (side)1

One side is (2x +7)

Answer:

o

0 F x>o v 0 cover the interval (-4,-3

The statement which is true about the graphed function is that F(x) > 0 over the interval (-∞, -4).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a graph of a function.

The options contains the open interval (-∞, -3) and (-∞, -4).

It is clear that along this interval, the graph is situated above the X axis.

This means that the values of y is all greater than 0.

At x = -4, F(x) = 0

For all x < -4, F(x) > 0

So the correct statement is F(x) > 0 over the interval (-∞, -4).

Hence F(x) > 0 over the interval (-∞, -4).

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Answer:

We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:

(length of kite) / (length of shadow) = (height of kite) / (length of shadow)

x / 9 = 10 / 9

To solve for x, we can cross-multiply and simplify:

x = 90 / 9

x = 10

Therefore, the length of the kite's line is 10 feet.

Step-by-step explanation:

Answer:

Which statements can be used to justify the fact that two right angles are supplementary? Select two options.

*  A right angle measures 90°.

If two angles are complementary, the sum of the angles is 90°.

* If two angles are supplementary, the sum of the angles is 180°.

A complementary angle is one-half the measure of a supplementary angle.

A supplementary angle is twice the measure of a complementary angle.

Step-by-step explanation:

(A) and (C)

A right angle measures 90°, hence the sum of two right angles is 180° (supplementary)

An angle is formed when two lines intersect each other. Two angles are said to be supplementary if their measures add up to 180 degrees while Two angles are called complementary if their measures add up to 90 degrees.

To justify the fact that two right angles are supplementary. Firstly a right angle measures 90°, hence the sum of two right angles is 180° (supplementary)

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Answer:36

Step-by-step explanation: 3X4 or 3 rectangles plus tow rectanges that = 12

Answer:

Each friend raised $ 182.50.

Step-by-step explanation:

Given that four friends raised a total of $ 730 for a local charity, and each friend raised the same amount of money, for model the total amount that the friends raised the following calculation must be performed:

730/4 = X

182.5 = X

Therefore, each friend raised $ 182.50.

Answer:

2x^2 −12x+17

Step-by-step explanation:

i think i did that right?

The value of the basket in 2018 was $92.48 if the basket contains 15 lollipops, 10 bars of chocolate, four jars of peanut butter, and two ice-cream cakes.

The value of the basket in 2018 can be calculated by using multiplication and addition.

First, we multiply the cost of each good in 2018 by the number of that good in the basket to calculate their total cost.

Lollipop: $0.80 × 15 = $12

Chocolate: $3.75 × 10 = $37.5

Peanut butter: $4.25 × 4 = $17

Ice-cream cake: $12.99 × 2 = $25.98

Now the value of the basket in 2018 can be calculated by adding these amounts of each good. Therefore;

Value of basket = $12 + $37.5 + $17 + $25.98

Value of basket = $92.48

Hence the value of the basket in 2018 is $92.48

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The least number of trips that Ava must make in order to deliver 250 cartons of books is 10 trips.

The least number of trips that Ava must make in order to deliver 250 cartons of books can be found by dividing the total number of cartons by the number of cartons that her car can hold per trip.

This can be written as:
Least number of trips = Total number of cartons / Number of cartons per trip

Substituting the given values into the equation, we get:
Least number of trips = 250 cartons / 26 cartons
Least number of trips = 9.62

Since Ava cannot make a fraction of a trip, we need to round up to the nearest whole number. Therefore, the least number of trips that Ava must make in order to deliver 250 cartons of books is 10.

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(Hey, angles rock!)

Answer:

45 + 60 = 105

Step-by-step explanation:

ABC consists of two angles, angle ABD and angle DBC. Therefore, the sum of the measures of angles ABD and DBC is the measure of ABC.

45 + 60 = 105

Step-by-step explanation:

first fine 2% of the initial salary since he is paid that every year

2/100×69400=2×694=1388

so for 17 years = 1388×17

=23596

Answer:

i believe your answer is.

4,789,658,950

Step-by-step explanation:

For a uniform distribution random variable X, the probability that the random variable has a value between 0.6 and 2.1 is equals to 0.1875. So, option(a) is right one.

The uniform distribution is defined as a continuous probability distribution and the events are equally likely to occur. In other words in this distribution every possible outcome has an equal probability. There is a uniform distribution of variable. Let the random variable be denoted by X be uniformly distributed. The above figure shows uniform density curve for X. That is \( X \: \tilde \: \: U( 0, 8) \).

Probability density function is f(x) = \(\frac{ 1}{8} = 0.125\)

We have to determine probability that the random variable has a value between 0.6 and 2.1, P(0.6 ≤ X ≤ 2.1). So, required probability is P(0.6 ≤ X ≤ 2.1) = \(\int_{0.6}^{2.1} f(x) dx \).

\(= [ 0.125x ]_{0.6}^{2.1}\)

= 0.125 ( 2.1 - 0.6)

= 0.125 ( 1.5)

= 0.1875

Hence, required value is 0.1875.

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Complete question:

the above figure complete the question.

Using the uniform distribution density curve answer the question :

what is the probability that the random variable has a value between 0.6 and 2.1?

a) 0.1875

b) 0.4625

c) 0.3375

d) 0.2125

Answer:

4, 2, 8

Step-by-step explanation: